Problem: Nadia is 10 years younger than Kevin. Kevin and Nadia first met 3 years ago. Seventeen years ago, Kevin was 3 times older than Nadia. How old is Kevin now?
Explanation: We can use the given information to write down two equations that describe the ages of Kevin and Nadia. Let Kevin's current age be $k$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $k = n + 10$ Seventeen years ago, Kevin was $k - 17$ years old, and Nadia was $n - 17$ years old. The information in the second sentence can be expressed in the following equation: $k - 17 = 3(n - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $n$ and substitute it into our second equation. Solving our first equation for $n$ , we get: $n = k - 10$ . Substituting this into our second equation, we get the equation: $k - 17 = 3($ $(k - 10)$ $ -$ $ 17)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 17 = 3k - 81$ Solving for $k$ , we get: $2 k = 64$ $k = 32$.